Parallel axis

Definition

The parallel axis theorem is used to determine the moment of inertia of a rigid body about any axis, given the moment of inertia about a parallel axis through its center of mass and the distance between these axes.

5 Must Know Facts For Your Next Test

1. The parallel axis theorem states that $I = I_{cm} + Md^2$, where $I$ is the moment of inertia about the new axis, $I_{cm}$ is the moment of inertia about the center of mass, $M$ is the mass of the object, and $d$ is the distance between the two axes.
2. This theorem applies only to rigid bodies.
3. The parallel axis theorem simplifies complex calculations by using known moments of inertia for standard shapes.
4. It is crucial for calculating rotational dynamics in systems where an object's rotation does not occur around its center of mass.
5. The theorem can be used in combination with other methods to derive moments of inertia for composite objects.

Review Questions

• What is the formula stated by the parallel axis theorem?
• Why is knowing the moment of inertia about an object's center of mass important when using the parallel axis theorem?
• In what scenarios would you apply the parallel axis theorem?

Related terms

Moment of Inertia:

A measure of an object's resistance to changes in its rotational motion around a particular axis.

Center of Mass:

The point at which an object's mass can be considered to be concentrated for analysis purposes.

Rigid Body:

An object with a fixed shape that does not deform under stress or force.